Methods and apparatus for determining position



March 31, 1959 s. w. wlLcox ETAL 2,880,413

METHODS AND APPARATUS FOR DETERMINING POSITION Filed Aug. 28, 195s i 2Sheets-Sheet 1 1 .whs E March 31, 1959 's. w. wlLcox ETAL ME'IHODS ANDAPPARATUS FOR DETERMINIG POSITION Filed Aug. 28, 1953 2 Sheets-Sheet 2United States Patent METHODS AND APPARATUS FOR DETERMINING PSITIONStanley W. Wilcox and Warren B. Garrison, Tulsa, Okla., assignors toSeismograph Service Corporation, Tulsa, Okla., a corporation of DelawareApplication August 28, 1953, Serial No. 377,094

24 Claims. (Cl. 343-105) The present invention relates to radio positionfinding systems and more particularly to methods and apparatus for usein radio position finding systems employing phase comparison in pairs ofposition indication signals radiated from a plurality of spacedtransmitting points to provide indications from which the position of amobile receiving point relative to the known positions of thetransmitting points may be determined.

In systems of the particular type referred to, the continuous wavesradiated from each pair of transmitters produce standing waves in space,the phase relationship of which changes as aV function of changingposition between the two transmitting points. More specifically, thestanding waves produced by each pair of transmitting units of the systemare characterized by isophase lines which are hyperbolic in contourabout the transmitting points as foci. On a line connecting the pair oftransmitters, these isophase lines are spaced apart a distance equal toone-half the mean wave length of the radiated waves and have divergingspacings at points on either side of this line. With this systemarrangement, the position of a receiving point relative to a pair ofhyperbolic isophase lines may be determined by measuring the phaserelationship between continuous waves radiated from the pair oftransmitters.

Since the point of location of the receiving point along the zoneseparating the two isophase lines is not indicated by such a phasemeasurement, it becomes necessary to employ at least three spacedtransmitters, different pairs of which function to provide a grid-likepattern of intersecting hyperbolic lines, in order to obtain absolutedetermination of the position of the receiving point. Systems of thecharacter described are exceedingly accurate insofar as the positionindications produced at the receiving point are concerned. To obtain thedesired indication accuracy, however, it is necessary to maintain phasesynchronization between the continuous waves radiated by the spacedtransmitters, or alternatively, so to arrange the system that phaseshifts between the radiated waves are compensated during the phasecomparing operation.

In Honore Patent No. 2,148,267 a system is disclosed in which thecarrier waves of each pair of transmitters are heterodyned at a fixedlink transmitting point, and the dilference frequency component of theheterodyned waves is modulated as a reference signal upon the carrieroutput of the link transmitter for radiation to the receiving point,where the difference frequency component is detected and phase comparedwith a difference frequency signal derived by directly heterodyning thetransmitted continuous waves at the receiving point. In this manner,phase shifts between the continuous waves radiated from the twotransmitters are completely compensated so that the measured phase angleis truly representative of the location of the receiving point between apair of isophase lines. In Hawkins and Finn U. S. Patent 2,513,317 animproved system is disclosed wherein a pair of transmitters arealternately operated as link transmitters and as position signaltransmitters thereby reducing the num- ICC ber of signal channelsrequired. It is desirable that the channel frequencies employed belocated adjacent the broadcast band or at least below the ultra-highfrequency band in order to obviate the problem of line-of-sighttransmission, which of course necessitates the location of a number ofchannel frequencies in the most crowded portion o-f the frequencyspectrum, at least insofar as operations in the United States areconcerned. Since frequency allocations in this band must be maintainedVat a minimum, it is highly desirable to provide a position determiningsystem which reduces the number of channels required.

Another problem encountered in the operation of continuous wave systemsis that of eliminating ambiguity from the phase measurements whichprovide the desired position information. Thus while the two phasemeasurements identify the position of the receiving station relative totwo intersecting pairs of hyperbolic isophase lines, they do notindicate the particular pairs of lines to which the indications arerelated. This means that in operating the system the geographic locationof the receiving system must be known at the start of movement of thereceiving system relative to the transmitting stations and, furthermore,that the successive wave lengths must be counted as the receivingstation is moved relative to the grid-like pattern of hyperbolic lines.It also means that a mobile craft entering the radiation pattern of thetransmitters cannot utilize the radiated signals to determine itsposition without employing auxiliary equipment to determine theapproximate position of the craft relative to the signal transmitters.

In a copending application Serial No. 138,235, filed January 12, 1950,entitled Radio Location System, now U. S. Patent No. 2,652,558, grantedSeptember 15, 1953, and assigned to the same assignee as the presentinvention, there is disclosed an improved radio location system of thecontinuous wave type which is free not only of phase synchronizationdifficulties but also of ambiguity problems. In the system of the saidcopending application, position indications are obtained havingdifferent sensitivities, termed phase sensitivities, insofar as thespacing of the isophase lines is concerned. More specifically, aplurality of low phase sensitivity position indications and a pluralityof high phase sensitivity position indications are obtained, the lowphase sensitivity indications being effective to locate the range of thehigh phase sensitivity indications and being characterized by widelyspaced phase coincidences and the high phase sensitivity indicationsbeing characterized by closely spaced phase coincidences. The high andlow phase sensitivity indications are obtained by producing pairs ofbeat frequency signals in accordance with the principles of the Honoresystem" and then heterodyning these beat frequency signals to produceposition indicating and reference signals for phase comparison whichhave phase sensitivities determined by phantom frequencies correspondingto the sum of or difference between the mean frequencies of the carrierwaves from which the pairs of beat frequency signals were derived.

While this latter system completely sovles the ambiguity problem, aconsiderable number of transmitters and carrier channels are requiredand a number of narrow band pass filters must be employed to separatethe various position indicating and reference signals, which adds to theexpense and may cause phase shift difiiculties unless the band passfilters are carefully selected and balanced. In United States Patent2,629,091 entitled Radio Location System, issued February 17, 1953,there is disclosed and claimed an improved radio location system of thecontinuous wave type which is free of phase synchronization diicultiesof the character mentioned, in which the above mentioned disadvantagespertaining to ambiguity are entirely obviated, and in which the use ofnarrow band pass filters is minimized or eliminated.

However, all of the proposed systems for resolving ambiguity haveinvolved the use of at least one additional channel frequency as well asadditional equipment at either or both of the transmitting and receivingends of the systems. In accordance with the present invention acompletely non-ambiguous position determining system is provided withoututilizing an additional frequency channel and without altering thetransmitting equipment. It is an object of the present invention,therefore, to provide an improved radio location system of the aboveindicated type in which disadvantages pertaining to ambiguity areentirely obviated.

It is a further object of the present invention to provide an improvedradio location system of the continuous wave type in which the abovementioned difficulties in providing ambiguity resolution are eliminatedand which at the same time combines economy of channel frequencies withminimum cost of the equipment.

It is another object of the invention to provide an improved radiolocation system of the continuous wave type which affords a solution tothe ambiguity problem without employing an additional channel frequencyand without altering the transmitting equipment for establishing anaccurate fix.

It is a still further object of the present invention tov provideimproved receiving equipment for use in radio location systems of theabove-indicated character.

It is likewise an object of the present invention to provide a methodfor determining the approximate location of a mobile unit positionedwithin a hyperbolic field pattern.

lt is still another object of the invention to provide a method fordetermining the approximate position of a mobile unit in a continuouswave iield pattern which includes the step of measuring the rate ofdivergence of the hyperbolic lines at the unknown position.

The invention both as to its organization and method of operation,together with further objects and advantages thereof will best beunderstood by reference to the specification, taken in conjunction withthe accompany ing drawings in which:

Fig. 1 is a pictorial representation of a water-covered area over whichsurvey operations are to be performed illustrating one positionalarrangement of the transmitters embodied in the system and the grid-likepattern of isophase lines effectively produced in space by the signals yradiated by the transmitters;

Fig. 2 diagrammatically illustrates one pair of the transmitters shownin Fig. 1 with the hyperbolic isophase lines existing therebetween andincludes a plurality of curves defined by movement of the mobilereceiving unit in predetermined relationship with respect to thehyperbolic lines;

Fig. 3 is a diagrammatic illustration of one form of mobile receivingequipment that may be employed in the system of Fig. l; and

Fig. 4 diagrammatically illustrates one positional arrangement of theantennas at the mobile receiving unit which may be employed in thepractice of the present invention.

Referring now to Fig. l of the drawings, the invention is illustrated asembodied in a three-foci hyperbolic continuous wave system which ispreferably of the type disclosed and claimed in the above-identifiedHawkins and Finn Patent No. 2,513,317, but which may be of any othertype well-known in the art for providing position information at amobile receiving unit 13 carried by a vessel or vehicle 14 operatingwithin the radius of transmission of a plurality of spaced transmittingunits 10, 11 and 12. These transmitting units are preferably spacedapart approximately equal distances and are so positioned that the baseline 15 joining the points of location of the units and 11 is angularlyrelated to the base line 16 joining the points of location of the units11 and 12. The purpose of the transmitting units 10, 11 and 12 is toradiate position indicating signals in the form of carrier waves whicheffectively produce within the survey area an intersecting pattern ofhyperbolic lines, as indicated by the reference characters 17 and 18,the family of hyperbolas indicated by the numeral 17 being produced as aresult of carrier wave radiation by the transmitting units 10 and 11 andthe hyperbolic lines designated 18 resulting from carrier wave radiationby the units 1l and 12. Both of the families of hyperbolas 17 and 18 arecharacterized by isophase lines that are spaced relatively closetogether on the base lines 15 and 16 interconnecting the transmittingunits and that diverge on either side of these base lines. Thedivergence of the hypcrbolas constituting the grid-like pattern is afunction of the distance from the base lines joining the units. Inaccordance with the present invention measurement of the expansion ofthe hyperbolic lines at any point in the radiation pattern of thetransmitting units 10, 11 and 12 provides a coarse positiondetermination which identifies the particular lane between adjacentisophase lines within which the receiving unit 13 is located. Anaccurate iix of the position of the mobile unit within this lane may beattained by the use of conventional receiving and indicating equipment,such as that described and claimed in the above-identified Patent2,513,317.

Referring now to Fig. 2, which illustrates a single pair of transmittingunits 10 and 11 and the family of hyperbolic lines 17 having foci at theunits, let it be assumed that the mobile receiving unit 13 is positionedat any point P within the radius of transmission of the signals radiatedby the transmitters at the units 10 and 11. Assume also that the carrierwaves radiated by the transmitters at the units 10 and 11 are eitherphase synchonized by any suitable phase synchronizing system or,alternatively, a reference transmitter is employed in accordance withthe principles enunciated in the above identitied Honore patent in orderto obviate phase synchronization diculties. The isophase lines 17 arespaced apart on the base line 15 by a phase difference of 360 electricaldegrees and by a distance corresponding to one-half wave length of themean frequency between the carrier waves radiated by the transmitters atthe units 10 and 11.

Consider first a single receiving antenna at the receiving unit 13employed to measure the phase of signals received at differencelocations in the hyperbolic pattern established by the transmittingunits. The relationship between the phase of two signals received at twodifferent locations may be expressed as:

is the average rate of change of phase in the direction determined bythe alignment of points P1 and P2 with respect to the hyperbolic field.In hyperbolic systems employing phase measurements at two spacedreceiving points in which the phase difference between the receivedsignals is obtained, the resulting indication is actually representativeof the average change of phase between the two receiving points. Thelimit of the phase difference, py-4t2, as AL approaches zero, or as thetwo receiving points are moved very close together, is the rate ofchange of phase in a given direction. Manifestly two such receivingpoints may be constituted by a pair of antennas spaced apart at anydesired distance aboard the vessel 14 thus controlling the magnitude ofthe quantity AL in Equation 1A.

If the mobile vessel or vehicle 14 is provided with a pair of antennasspaced apart at a fixed distance L, the phase difference between thesignals from the transmitters at the units and 11 received at each ofthese antennas will be dependent upon the alignment of the antennas withrespect to transmitting units 10 and 11 and also upon the position ofthe vessel 14 in the iield pattern, i.e., upon the divergence of thehyperbolas effectively provided in space. More particularly, if twospaced antennas designated by the reference characters 19 and 20 in Fig.1 and positioned at opposite ends of the vessel or vehicle 14, arealigned along the base line 15 (Fig. 2), the phase difference, 45p, indegrees between the signals received at the two antennas may beexpressed as:

L o P360 (l) in which Lis the spacing between antennas in appropriateunits of measurement and M2 is the half wave length of the meanfrequency of the carrier waves radiated by the units 10 and 11 expressedin the same units of measurement.

' Thus if the antennas are spaced apart a quarter wave length, a phasedifference of 180 exists between the signals received by these antennaswhen aligned along the base line 15. If the antennas are positionedequidistant from the base line 15 so that the line interconnecting themis perpendicular to the base line, the signals received by the antennasare in phase since the waves from the respective transmitters of theunits 10 and 11 travel equal distances to the antennas. Obviously thenthe phase difference of the received signals is dependent upon thealignment of the antennas with respect to the hyperbolic lines 17 aswell as the distance of the vessel 14 from the base line 15. I

When the mobile receiving unit 13 is positioned at point P as shown inFig. 2, the phase difference between signals received by the two spacedantennas varies from a maximum when the line joining the antennas isperpendicular to the hyperbolic line along which the receiving unit islocated to a minimum when the line joining the two antennas isapproximately coincident with that particular hyperbola.

The maximum phase difference between the signals received at the twoantennas occurs when the line joining them is perpendicular to thehyperbolic curve. Thus, if the receiving unit is moved from point Palong a path defined by the ellipse designated by the referencecharacter 21 in Fig. 2, a maximum phase difference between signalsreceived at the two antennas will be maintained. The elliptical paththus traversed is termed the ellipse orthogonal to the hyperbola passingthrough the point P. The magnitude of this maximum phase difference isnot a constant when the unit follows the elliptical path but insteadvaries from zero on the base line extensions 15 to a maximum along thedegenerate hyperbola 17 bisecting the base line 15.

If the phase difference is maintained constant as the mobile receivingunit moves from the point P, the path followed by the unit will be acircle 22 defined by the point P and the points of location of the twotransmitting units 10 and 11, the circle passing through the three namedpoints and being designated as a constant expansion circle. The constantexpansion circle may thus be dened as the locus of a point moving atconstant speed so as to cross the hyperbolic lines produced in spacebetween the units 10 and 11 at an equal rate, thereby following a pathat which the expansion factor of the hyperbolas is constant. Inaccordance with the present invention, measurement of the phasedifference existing between signals received at the spaced receivingpoints provides a means for ascertaining the particular expansion circlealong which the mobile receiving unit is positioned.

The expansion factor, which is a measure of the rate of divergence ofthe hyperbolas, may be defined as the ratio of the lane width at anypoint P in the survey area to the lane width along the base line and inequation form may be expressed as:

LW M2? (2) where E is the expansion factor; LWP is the lane width atpoint P; and M2 is the line width along the base line. The lane width atany point is the distance which must be traversed at right angles to thehyperbola in order to effect a complete 360 phase change in the signalsreceived by one of the antennas at the mobile receiving unit. Moregenerally, using two spaced antennas for receiving the radiated waves,the expansion factor may be expressed by the ratio of the maximum phasedifference between received signals at the base line, i.e., when theantennas are aligned along the base line, to the maximum phasedifference between the signals received by the antennas at any point P,i.e., when the line joining the antennas is perpendicular to thehyperbola through P. Mathematically this relationship may be expressedas:

P (3) in which E is the expansion factor, and 45B and :pp are the phasedifferences existing between receiving points spaced apart a iixeddistance L along the base line and in space, respectively. From equation(1) this may be reduced to:

Since L may be determined by measurement of the linear distance betweenantennas and A may be ascertained from the known transmittingfrequencies of the transmitters at the units 10 and 11, a measurement ofthe phase difference at point P in order to measure pp provides suicientinformation to enable the above equation to be solved for E, theexpansion factor. Both L and A will remain a constant for any giveninstallation having transmitting units operating at constant frequencyand with antennas at the vessel or vehicle 14 spaced a fixed distanceapart and, therefore, the Equation 4 becomes:

k E P for any particular system. Thus, it becomes apparent that asolution for the expansion factor may be readily effected by merelyspacing two antennas apart and measuring the maximum phase diiferencebetween signals radiated from the transmitting units 10 and 11.

To permit the constant expansion circle to be constructed after theexpansion factor E has been computed, it should be appreciated fromEquation 2 that the expression for the lane width at any point P is:

LWP= (5) 2 SIl 2- in which 1 E sin A/2 and A represents the angleincluded between the lines r1 and r2 interconnecting the point P withthe foci of the hyperbolas f1 and f2 positioned respectively at thepoints of location of the transmitting units 10 and 11. The angle Aremains constant irrespective of the position along the constantexpansion circle 22 occupied by the mobile receiving unit inasmuch asthe lines r1 and r3 encompass the same arc portion as illustrated by thedotted line portion 22' of the extended constant expansion circle. Thetangent 23 to the hyperbola passing through the point P bisects theangle A and thus divides this angle into two equal portions having amagnitude of A/ 2 which manifestly also remains constant as the point Pmoves along the circular path 22. Since A/2 is a constant for any pointon the constant expansion circle, the expansion factor E is also aconstant for any point on this curve.

The relationship between the expansion factor E and the angle A/ 2 atthe point P0, defined by the intersection of the constant expansioncircle 22 and the degenerate hyperbola 17' bisecting the base line 15,enables the construction of the constant expansion circle from the valueof E ascertained by measuring the phase difference qbp at the positionoccupied by the mobile receiver. At the point P it is apparent that:

in which C represents one-half of the base line length between thetransmitting units 10 and 11 located at foci f1 and f2, respectively,and flPo represents the distance from foci f1 to the point P0 on thedegenerate hyperbola. From Equation 5 in which The value of theexpansion factor having been determined as indicated above by measuringthe phase difierence pp between signals received at the antennas and thevalue of C being a measurable quantity which is a constant for anyparticular set of transmitting units, it is possible to calculate thevalue of CE. On a hyperbolic chart displaying the position oi theisophase lines 17 in their geographic relationship to the knownpositions of the transmitting units and 11 a compass may be positionedat the location of either of the transmitting units and an are may bestruck having a radius equal to CE. The intersection of the arc struckas just described with the degenerate hyperbola 17 locates the point P0and thus establishes three points on the constant expansion circle 22.The center of the constant expansion circle may be located by drawingthe perpendicular bisector to the chord of the circle flPo whichbisector will intersect the degenerate hyperbola 17', the perpendicularbisector of a second chord constituted by the base line 15, at thecenter of the circle. Having established the center of the circle, acompass may be employed to draw the complete constant expansion circle22 through the points f1, f2 and P0. It, therefore, becomes apparentthat the measurement of the phase difference between the signalsreceived at spaced positions together with a knowledge of the dimensionsand frequencies of operation of the transmitting system providesufficient information to es tablish the particular expansion circlealong which the mobile receiving unit is located.

The position information thus derived is ambiguous in the sense that themeasurement of the phase difference at the two antennas between positionindicating signals radiated by the transmitters at the units 10 and 11does not define the particular position on the expansion circle at whichthe mobile unit is located. Identification of this position isaccomplished by measuring the maximum phase diierence received at thetwo spaced receiving points from carrier waves radiated by thetransmitting units 11 and 12. By measuring the latter phase difference asecond expansion circle passing through the points of location of thetransmitting units 11 and 12 and through the point P at which thereceiving unit is located may be constructed in the manner indicatedabove. The intersection of the two constant expansion circles determinesthe location of the point P in space with an accuracy dependent upon theaccuracy of the measurement of the phase differences at the mobilereceiving unit. Since this accuracy is somewhat limited due to the smallphase differences which exist between antennas spaced relatively closetogether on board a ship or the like, the position determination is onlyan approximation of the location of the mobile receiving unit. The exactlocation may be determined as indicated above by directly comparing thecarrier waves radiated by the transmitting units 10, 11 and 12 in amanner well known in the art. The approximation derived fromconstructing the expansion circles, however, enables a determination ofthe lane within which the receiving unit is positioned and, therefore,resolves the ambiguity inherent in the accurate phase measurements.

The accuracy of the coarse phase difference measurements may beincreased by increasing the distance between the spaced antennas therebyproviding a larger phase difference between the signals received or byincreasing the base line length or spacing between transmitting units inorder to decrease the rate of divergence of the hyperbolas. The maximumspacing between antennas, particularly for shipboard installations, islimited by the size of the vessel or vehicle 14 carrying the mobilereceiving equipment and, therefore, the only practical method ofimproving the accuracy of the coarse phase measurements is to increasethe base line length. Since the maximum phase difference between signalsappearing at the two antennas varies from a maximum at the base line tozero at an iniinite distance from the base line, it is apparent that thealteration of the base line length to decrease the rate of divergence ofthe hyperbolas does not actually increase the accuracy of the phasedifference readings at the receiving unit but in effect causes the phasedifference to approach zero value at a slower rate. Thus the increasedbase line length increases the accuracy of the phase difference readingsat a given distance from the base line thereby increasing the areawithin which these phase difference readings are sufficiently accurateto locate the receiving unit within one of the lanes of the isophaselines produced by carrier wave radiation from the lspaced transmittingunits.

One type of mobile receiving equipment which may be employed to measurethe phase difference between signals received at the pairs of spacedantennas 19 and 20, and 19 and 20 in order to provide coarse positionmeasurements and which may also be employed to provide indicationsrepresentative of the fine or accurate phase position of the vessel 14is illustrated in Fig. 3 as comprising a plurality of fixed tunedreceivers 24, 25, 26 and 27, a plurality of band pass filters 28, 29,30, 31, 32 and 33, and a plurality of phase meters 34, 35, 36 and 37.This receiving equipment is adapted to receive the position indicatingsignals and the reference signals radiated by the transmitting units 10,11 and 12 which, as indicated above, may be of the type described inHawkins and Finn Patent 2,513,317 and which may be rendered operative toradiate carrier signals at the frequencies specified in that patent.

As therein described, the transmitting units 10 and 12 are continuouslyoperating to radiate carrier waves of different frequency which may beintermittently modulated with reference signals during appropriatespaced intervals of operation, whereas the unit 11 is adapted to radiatealternately a pair of position indicating signals in the form of carrierwaves of different frequencies during the spaced intervals. Thereceiving equipment for providing the fine or accurate phaseindications, is of the type described in Patent 2,513,317 and in Fig. 3is represented by the component elements of the block diagram drawn insolid lines. The equipment which has been added to the receiving unitdescribed in the indicated patent in accordance with the presentinvention to provide measurements of the phase difference existingbetween signals received at the spaced antennas is represented by thosecomponent elements indicated by the dotted lines in Fig. 3.

When the transmitter at the unit 10 and the transmitter of the unit 11are operating to radiate position indicating signals at frequencies of1700.300 and 1699.700 kilocycles, respectively, the transmitter at theunit 12 is operative to radiate a carrier wave at a frequency of1602.125 kilocycles which is modulated by a reference signal of 600cycles equal to the difference frequency between the signals radiated bythe operating transmitters at the units 10 and 11. The receiver 25 iscenter tuned to a frequency of 1602.000 kilocycles and thus, asindicated by the solid line arrow 40, receives the modulated carrierwave radiated by the transmitter at the unit 12. The 600 cyclemodulation component is reproduced by the receiver 25 and appliedthrough the band pass filter 31 center tuned to a frequency of 600cycles to the right hand set of input terminals of the phase meter 35.The receiver 24 is center tuned to a frequency of 1700.000 kilocyclesand thus, as indicated by solid line arrows 38 and 39, the carrier wavesradiated by the operating transmitters at the units 10 and 11 areaccepted by this receiver and heterodyned to reproduce the 600 cyclebeat frequency signal which is applied through the band pass filter 30to the left hand set of input terminals of the phase meter 35. Thismeter is, therefore, energized by signals of identical frequency and theresulting indication of the phase relationship between applied signalsis representative of the accurate position of the vessel 14 betweenadjacent isophase lines spaced relatively close together and effectivelyproduced in space by the carrier waves radiated by the operatingtransmitters at the units 10 and 11.

The output of the band pass filter 30, a 600 cycle signal resulting fromthe heterodyningof the position indicated signals radiated by theoperating transmitters at the units 10 and 11, is also applied to theleft hand set of input terminals of the phase meter 37. During this sameinterval, as indicated by solid line arrows 41 and 42, the antenna 20,spaced a fixed distance L from the point of reception of the antenna 19is energized by both of the carrier waves radiated by the transmittersof the units 10 and 11. These carrier waves are heterodyned by thereceiver 27 in order to produce a 600 cycle beat frequency signal whichis applied through the band pass filter 33 to the right hand set ofinput terminals of the phase meter 37. The phase meter 37, therefore,functions to measure the phase difference between the heterodyne signalsapplied to its opposite sets of input terminals. Inasmuch as thesesignals were produced by carrier waves radiated from the sametransmitters at the units 10 and 11, phase shift difficulties arelcompletely obviated and the phase meter 37, therefore, provides anindication which is representative of the difference between signalsreceived at the antennas 19 and 20 due solely to the difference intravel time of the radiated waves between the two reception points.

During the second interval of operation the transmitting unit 11 isrendered operative to radiate a second position indicating signal at afrequency of 1601.875 kilocycles, the transmitter at the unit 10radiates an unmodulated 1602.125 kilocycle carrier wave and thetransmitter at the unit 10 is operative to radiate a 1700.300 kilocyclecarrier wave which is modulated by the 250 cycle difference frequencybetween the signals radiated by the operating transmitters at the units11 and 12. The modulated carrier wave radiated by the unit 10 asindicated by the dotted line arrow 43 is received by the receiver 24 andthe 250 cycle modulation component developed at the output terminals ofthis receiver is applied through the band pass filter 28 to the lefthand 10 set of terminals of the phase meter 34. The position indicatingsignals radiated by the operating transmitters at the units 11 and 12during this interval are received as indicated by the dotted line arrows44 and 45 at the antenna 20 positioned closely adjacent to the antenna20 and at the fixed distance L from the antenna 19. The two carrierwaves appearing at this antenna are heterodyned by the receiver 25 inorder to produce a 250 cycle beat frequency signal which is appliedthrough the band pass filter 29 to the right hand set of input terminalsof the phase meter 34 where it is phase compared with the referencesignal applied to the opposite set of input terminals. The resultingindication on this phase meter is accurately representative of theposition of the vessel 14 between adjacent isophase lines effectivelyproduced in space by the carrier waves radiated by the operatingtransmitters at the units 11 and 12 during the second interval ofoperation.

The 250 cycle heterodyne signal passed by the band pass filter 29 isalso applied to the left hand set of input terminals of the phase meter36. During this same interval, as indicated by dotted line arrows 46 and47, the antenna 19', positioned closely adjacent the antenna 19 and at afixed distance L from the antenna 20, is energized by the carrier Wavesradiated by the operating transmitters at the units 11 and 12. These twocarrier waves are heterodyned by the receiver 26 in order to reproduce a250 cycle difference frequency signal which is applied through the bandpass filter 32 to the right hand set of input terminals of the phasemeter 36. Since the signals heterodyned at the antenna 19 and at theantenna 20' both emanated from the carrier waves radiated by thetransmitters at the units 11 and 12, any phase shift error in thecarrier waves will be transmitted over dual paths thus insuring that theindication on the phase meter 36 accurately portrays the phasedifference between signals received at the spaced antennas due solely tothe difference in travel time of the carrier waves. It thus becomesapparent that the indications on the phase meters 34 and 35 accuratelydefine the phase position of the vessel 14 between adjacent hyperboliclines 17 and 18, respectively, of the hyperbolic grid produced in thesurvey area. Manifestly from the math ematical derivations above, if thephase differences indicated on the meters 36 and 37 were maximized, itwould be possible to construct the expansion circles to obtain anapproximate position determination of the vessel 14 in order toascertain between which of the pairs of adjacent isophase lines of thehyperbolic grid the vessel is located. In order to maximize the readingson the phase meters 36 and 37 the aligned pairs of antennas 19 and 20and 19 and 20 should be positioned approximately perpendicular to thehyperbolic line on which the vessel 14 is located. One method foreffecting a maximum reading on these phase meters would be to mount theantennas on a rotating pedestal which could be turned through 360 and toobserve the maximum phase readings on the meters 36 and 37 duringrotation. Obviously these maximum phase readings would occur at dlferentpositions in the rotation of the antennas inasmuch as the maximum phasereading on the meter 36 would result when the antennas were positionedperpendicular to one of the hyperbolas 18 and the maximum phase readingon the phase meter 37 would occur when the antennas were perpendicularlyaligned with respect to one of the hyperbolas 17. Generally, however,the use of a rotating pedestal would not be feasible due to the largespacing between antennas ordinarily employed in order to provide phasedifferences of measurable magnitude. A second method for obtaining themaximum phase differences is to turn the vessel 14 in as sharp a turn aspossible to effect a complete 360 rotation of the aligned pairs ofantennas. The maxi mum phase readings on the meters 36 and 37 may be 11observed as the position of the vessel 14 is altered. Having obtained areading of the maximum phase difference, Equation 4 may be solved forthe expansion factor and from the computed value of E the expansioncircles for the pairs of transmitting units may be constructed.

If desired the necessity for orienting each pair of spaced antennas withrespect to the hyperbolic lines 17 and 18 may be obviated by employingtwo mutually perpendicular aligned pairs of equally spaced antennas inan arrangement such as that shown in Fig. 4. The line 17 isrepresentative of one of the hyperbolic lines between the units and 11along which the vessel 14 is located and the line 50 represents thenormal to this hyperbolic line, which is also the position assumed by asingle pair of spaced antennas aligned with respect to the line 17 toprovide maximum phase difference between signals received thereby.

The four antennas are designated by the reference numerals 20a, 20b, 20cand 20d and are positioned at equally spaced points along thecircumference of an imaginary circle having its center at theintersection of the hyperbolic line 17 and the normal 50. The antennas20a and 20c are separated by a fixed distance L as are the antennas 20band 20d and each of these pairs of antennas is adapted to be connectedto phase difference measuring apparatus which may be of the typepreviously described and which functions to measure the phase differencebetween signals received at the spaced pairs of antennas.

If it is assumed that the number of electrical degrees of phasevariation on either side of the hyperbolic line 17 varies linearly withdistance, i.e., that the hyperbolic lines representative of each degreeof phase position are positioned equal distances apart within a limitedarea such as the span L between antennas, the variation may be expressedin terms of radians per foot and designated R.

The angle X represents the angle between an imaginary line 51interconnecting the antenna pair 20a and 20c and the normal line 50.Thus if the antennas were aligned so that the line 51 coincided with thenormal line 50, the meter reading, designated M1 on the phase measuringapparatus connected between the antennas 20a and 20c would be equal to(LR) radians, i.e., the total antenna span expressed in feet multipliedby the phase variation per foot. The meter reading M1 could obviously becalibrated to read radian measure instead of the conventionalmeasurement of electrical degrees. With antennas 20a and 20c in theposition just described it is apparent that the antennas 20b and 20dwould both be located practically coincident with the isophasehyperbolic line 17 and, therefore, the meter reading designated M2 ofthe phase measuring apparatus connected between these antennas would bezero. Obviously, the maximum phase difference between signals receivedby the pairs of antennas would be equal in magnitude to LR since this isthe phase difference encountered when each antenna pair isperpendicularly aligned with respect to the hyperbolic line 17.

When the antennas 20a and 20c occupy any position along the imaginarycircle to form the angle X between the line 51 and the line 50, thereading M1 on the phase measuring apparatus connected therebetween isequal to:

LR cos X (7) expressed in radians. The aligned pair of antennas 20b and20d are disposed at an angle of 90 with respect to the aligned pair 20aand 20c and thus the reading M2 of the phase measuring apparatusconnected between the former antenna pair may be expressed as LR cos(x4-90") in radians. The latter equation reduces by trigonometricsubstitution to:

M2=(LR) sin X From the two Equations 7 and 8:

M12=(LR)2 eos X but by trigonometric identity:

cos2 X-l-sin2 X=1 and, therefore:

Thus the maximum phase difference occurring between a single pair ofspaced antennas is equal to the square root of the sum of the squares ofthe individual phase differences between each pair of the alignedmutually perpendicular pairs of antennas irrespective of their angularorientation with respect to the hyperbolic pattern. The value of\/M12|M22 is of the same magnitude as the phase difference which wouldbe obtained by employing a single pair of antennas spaced apart adistance L and oriented in the hyperbolic field to produce a maximumphase difference. The individual phase readings thus provide informationfrom which the maximum phase difference may be computed Without alteringthe course of the vessel 14 and without stopping the progress of thesurvey being conducted.

Since the meter readings M1 and M2 are indicative only of the maximumvalue of the phase difference existing between signals at the vesselsradiated by the units 10 and 11 to form the hyperbolic pattern 17, it isnecessary to provide additional measuring equipment to provide similarreadings for the phase differences existing between signals received atthe vessel from the units 11 and 12. This additional equipment may be inthe form of a second set of aligned pairs of perpendicular antennas andan additional pair of phase measuring devices connected between theantenna pairs. Alternatively, this equipment may consist of additionalphase measuring apparatus connected to the antennas 20a, 20b, 20c and20d but which includes selective means for differentiating between thesignals radiated by the units 10 and 11 and those radiated by the units11 and 12.

From the above explanation it will be apparent that the presentinvention affords a satisfactory solution to the problem of resolvingambiguity and at the same time minimizes the number of frequencychannels required to form a complete radio position determining system.In addition, the described system provides an economy in the amount ofequipment required to form the cornplete transmitting and receivingapparatus. While the invention has been described in conjunction withradio position determining apparatus of the hyperbolic continuous wavetype, it should also be appreciated that other applications will arise,particularly in the field of navigation, in which the relative magnitudeof the phase difference existing between pairs of spaced antennas may beemployed to indicate the relative position of a mobile unit with respectto a hyperbolic field pattern. For instance, a mobile unit could bemaintained on an essentially elliptical course merely by maintaining amaximum phase difference between signals received at a pair of spacedantennas since the indication of a maximum phase difference isrepresentative of the ellipse orthogonal to the hyperbolic curve onwhich the mobile unit is located. Thus by insuring that each position ofthe mobile unit represents a maximum phase difference position, it isapparent that the course of the vessel would follow the ellipseorthogonal to all of the hyperbolic lines traversed. This maximum phasedifference could be maintained by means of the arrangement shown in Fig.4 by constantly orienting the position of the mobile unit so that themeter reading on the phase measuring apparatus connected betweenantennas 20b and 20d is constantly maintained at a zero value therebyinsuring that the phase measur- 13 ing apparatus connected between theantennas 20a and 20c will provide a maximum phase difference indicationand also insuring that the course of the vessel carrying the antennaswould follow the ellipse orthogonal to the hyperbolic curves forming thefield radiation pattern.

While particular embodiments of the invention have been shown, it willbe understood, of course, that the invention is not limited theretosince many modifications may be made, and it is therefore contemplatedby the appended claims to cover any such modifications as fall withinthe true spirit and scope of the invention.

What is claimed as new and desired to be secured by Letters Patent ofthe United States is:

1. A method of resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobile unitin a hyperbolic field pattern which comprises measuring the expansion ofthe hyperbolic lines at the location of the mobile unit, andgeometrically constructing the locus of all points of the hylperbolashaving an expansion equal to the measured va ue.

2. A method of resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobile unitin a hyperbolic field pattern which comprises measuring the expansion ofa first set of hyperbolic lines at the location of the mobile unit toobtain a first measured value, measuring the expansion of anintersecting second set of hyperbolic lines at the same location toobtain a second measured value, constructing a first geometric curverepresentative of the locus of all points of the first set of hyperbolashaving an expansion equal to the first measured value, and constructinga second geometric curve representative of the locus of all points ofthe second set of hyperbolas having an expansion equal to the secondmeasured value.

3. A method of resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobile unitin a hyperbolic field pattern which comprises measuring the expansion ofdifferent sets of hyperbolas of said hyperbolic pattern, andconstructing from the measured values a pair of constant expansioncircles representative of positions along said difierent sets ofhyperbolas at which the same expansion occurs.

4. A method of resolving ambiguity in radio location systems ofhyperbolic type by determining the approximate location of a mobile unitin a hyperbolic field pattern which comprises measuring the phasedifference between signals appearing at the location of the mobile unitby means including at least one antenna, moving said antenna relative tothe field pattern in order to obtain the maximum phase differencethereby providing a measure of the expansion of the hyperbolic lines atsaid mobile unit, and geometrically constructing the locus of all pointsin said pattern at which the maximum phase difference is equal to themeasured value.

5. A method of resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobile unitin a hyperbolic field pattern which comprises measuring the phasedifferences between pairs of signals appearing at the location of themobile unit by means including at least one antenna, moving said antennarelative to the field pattern in order to obtain the maximum phasedifferences between different pairs of said signals thereby providing ameasure of the expansions of different sets of hyperbolic linesconstituting said pattern, and constructing from the measured values apair of constant expansion circles representative of positions alongeach set of said hyperbolic lines at which the same maximum phasedifference occurs.

6. A method of resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobile unitin a hyperbolic field pattern which comprises measuring the phasedierence between a first pair of signals at the location of the mobileunit by means including at least one antenna, measuring the phasedifference between a second pair of signals appearing at the mobileunit, moving said antenna relative to the field pattern in order toobtain the maximum phase differences thereby providing measurements ofthe expansions of the hyperbolic lines at said mobile unit, andconstructing from the measured Values a` pair of constant expansioncircles representative of positions along each set of said hyperboliclines at which the same maximum phase difference occurs.

7. In a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, and means for measuring the expansion of thehyperbolic lines at the location of the mobile unit to provide anapproximate determination of the location of said unit.

8. In a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, means including a pair of spaced antennas formeasuring the phase difference between signals at said mobile unit, andmeans for maximizing the phase difference measurements to provide anindication of the expansion of the hyperbolic lines at the mobile unitthereby facilitating the determination of the approximate location ofthe unit.

9. In a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, and means for measuring the expansions of differentsets of hyperbolic lines in the field pattern at the location of themobile unit to provide an approximate determination of its location.

10. ln a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, means including a pair of spaced antennas formeasuring the phase differences between different pairs of signalsrepresentative of different sets of hyperbolic lines constituting saidpattern, and means for maximizing the phase difference measurements toprovide an indication of the expansion of the hyperbolic lines at themobile unit thereby facilitating the determination of its approximatelocation.

l1. Apparatus for resolving ambiguity in phase comparison systems of thehyperbolic type by determining the approximate location of a mobilereceiving unit with respect to sets of intersecting hyperbolic linesestablished by waves radiated from at least three spaced transmittingunits which comprises, spaced receiving means at said mobile unit formeasuring different phase positions of said unit with respect to eachset of hyperbolic lines, and means for measuring the phase differencesbetween signals received at each of said spaced receiving means in orderto provide an indication of the expansions of the different sets ofhyperbolic lines of said mobile unit.

12. Apparatus for resolving ambiguity in phase cornparison systems ofthe hyperbolic type by determining the approximate location of a mobilereceiving unit with respect to sets of intersecting hyperbolic linesestablished by waves radiated from at least three spaced transmittingunits which comprises, spaced receiving means at said mobile unit formeasuring different phase positions of said unit with respect to eachset of hyperbolic lines, means for measuring the phase differencesbetween signals received at each of said spaced receiving means, andmeans for maximizing the phase difference signals by moving the spacedreceiving means relative to said hyperbolic lines in order to obtain anindication of the expansions of different sets of hyperbolic lines atsaid mobile unit.

13. In a position determining system of the hyperbolic type employing amobile receiving unit positioned within a hyperbolic field pattern, thecombination of means for determining an accurate phase position of saidmobile unit with respect to different sets of hyperbolic lines of saidpattern, and means including spaced receptor points at said mobilereceiving unit for measuring the expansion of each of the sets ofhyperbolic lines at the location of the mobile unit to provide anapproximate determination of its location.

14. In a position determining system of the hyperbolic type employing amobile receiving unit positioned within a hyperbolic tield pattern, thecombination of means for determining an accurate phase position of saidmobile unit with respect to different sets of hyperbolic lines of saidpattern, means including a pair of spaced receptor points for measuringthe phase difference between signals received at said spaced receptorpoints, and means for determining the maximum phase difference betweensaid signals to provide an indication of the divergence of thehyperbolic lines thereby facilitating the determination of theapproximate location of said mobile unit.

15. In a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, and means including angularly disposed pairs ofspaced antennas for measuring the expansion of the hyperbolic lines atthe location of the mobile unit to provide an approximate determinationof the location of said unit.

16. In a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, means including angularly disposed pairs of spacedantennas for measuring the maximum phase difference between pairs ofsignals appearing at said antennas to provide an indication of theexpansion of the hyperbolic lines at the mobile unit therebyfacilitating the determination of the approximate location of the unit.

17. In a position determining system of the hyperbolic type employing amobile unit positioned at an unknown location with respect to ahyperbolic field pattern, the combination of means for determining anaccurate phase indication of the position of said mobile unit within thehyperbolic pattern, and means including at least two aligned pairs ofspaced antennas positioned so that one of said aligned pairs is disposedat right angles with respect to the other aligned pair for measuring themaximum phase differences between different pairs of signals received bysaid antennas and representative of different sets of hyperbolic linesconstituting said pattern, thereby providing an indication of theexpansion of the hyperbolic lines at the mobile unit in order tofacilitate the determination of its approximate location.

18. Apparatus for resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobilereceiving unit with respect to sets of intersecting hyperbolic linesestablished by waves radiated from at least three spaced transmittingunits which comprises pairs of receptor points angularly disposed withrespect to each other spaced at said mobile unit for receiving signalsrepresentative of different phase positions of said unit with respect toeach set of hyperbolic lines, and means for measuring the phasedifferences between signals received at each of said spaced receiving 16means in order to provide an indication ofthe expansions of thedifferent sets of hyperbolic lines at said mobile unit.

19. Apparatus for resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of a mobilereceiving unit with respect to sets of intersecting hyperbolic linesestablished by Waves radiated from at least three spaced transmittingunits which compriss aligned pairs of angularly disposed spaced receptorpoints at said mobile unit for receiving signals representative ofdifferent phase positions of said unit with respect to each set ofhyperbolic lines, means for measuring the phase differences betweensignals received at each of said aligned pairs of spaced receptor pointsin order to determine the maximum phase difference between the signalsappearing at said mobile unit thereby obtaining an indication of theexpansions of different sets of hyperbolic lines at the location of themobile unit.

20. In a hyperbolic radio location system, apparatus for ascertainingthe rate of divergence of the hyperbolic lines at an unknown locationestablished by radiations from spaced transmitting stations whichcomprises at least two spaced receiving antennas, means for developingfirst and second control signals each representative of the position ofa different one of said antennas with respect to the hyperbolic linesand means jointly responsive to said first and second control signalsfor indicating the rate of divergence of the hyperbolic lines in theregion of said antennas.

2l. In a hyperbolic radio location system, apparatus for ascertainingthe rate of divergence of the hyperbolic lines at an unknown location byradiation from spaced transmitting stations which comprises at least twospaced receiving antennas, means for indicating the phase differencebetween signals received at said antennas from said transmittingstations, and means for maximizing the phase difference indications inorder to determine the rate of divergence of the hyperbolic lines in theregion of said antennas.

22. In a hyperbolic radio location system, apparatus for ascertainingthe rate of divergence of the hyperbolic lines at an unknown locationwhich comprises at least two pairs of equally spaced mutuallyperpendicular receiving antennas, and means for indicating the phasedifference between signals received at each pair of antennas.

23. In a hyperbolic radio location system, apparatus for orienting amobile unit with respect to a hyperbolic field pattern established byspaced transmitters which comprises at least two spaced receivingantennas each of which receives signals radiated from said spacedtransmitters, means for developing a first signal representative of theposition of a first of said antennas relative to said transmitters,means for developing a second signal representative of the position ofthe second of said antennas relative to said transmitters, and meansjointly responsive to said rst and second signals for indicating thedivergence of the hyperbolic lines of said pattern at the mobile unit.

24. A method of resolving ambiguity in radio location systems of thehyperbolic type by determining the approximate location of the mobileunit in a hyperbolic field pattern which method comprises the steps ofmeasuring the expansion of the hyperbolic lines at the location of themobile unit, obtaining a line position indication representing theposition of the mobile unit, and utilizing the expansion measurement toobtain a coarse position determination representing the approximateposition of the m0- bile unit.

References Cited in the file of this patent UNITED STATES PATENTS2,531,908 Grenfell Nov. 28, 1950 2,592,459 Perilhou Apr. 8, 19522,608,685 Hastings Aug. 26, 1952 2,646,564 Perilhou July 21, 1953 UNITEDSTATES PATENT OEFCE CERTIFICATE OF CORRECTION Patent-NO'. 21,880,413March ,31, 1959 stanley W. wilcoxret ai.

It is hereby oertii'emv :that error appears in theprinted'Vspeoificution of the above numbered patent requiringoorreo'tion. andithat the' .said Let'rrs Patent should read as'tcorreoised ,belowu l Column -2, line 6 0., for "sovlersY rendsolyesxum;column 6, line l2,

for "line", first oocurrenoofy read lanewm; column 13, line` 46, afiserl "Systems of" insert They l-g column lo, line' 8, xfor Hcompriss" readcomprises Signed and sealeic this 25th day ofl August 1959@ C Ates'b: C

KAEL H., VMEINE Attesting officer Comissioner of Patents ROBERT C WATSONUNITED STATES PATENT QEFICE CERTIFICATE OF CORRECTION PamNo. 21,880,413March El, 1959 ,Stanley W, Wilcox et al.

It is hereby CertifiedA that error appears in the' printec'Ispecification of the above' numbered patent requiring Qcrreetion and.that the' said Lers Patent should read as correo-tecL below.

Column 2 line' 6U, for "sovles" read n solvesL fm; column 6, lin@ 129for "line", first occurrence, read E. lane ha; Column 13, lime 46, afterSystems of" insert the Column 16, line 8, lfor "compris's" readmccmprises (SEAL).

Attest:

mp3" WINE ROBERT c. WATSON 'b'bes'ting Officer v Com-hissoner of PatentsUNITED STATES PATENT OFFICE CERTIFICATE 0F CORRECTION Patent No.2,880,413 March 31, i959 Stanley Wb Wilcox et al.,

It is hereby certifiedl 'that error appears in the' printedspecification oi' the above numbered patent requiring Correctionv and.that the' ,said Lersrs Paten-b should read as corrected below Column 2,line o0, for Hsovles rend m soli/ssNr uw; column o, lin3 I2? for "line",first occurrence?y read lans su; Column 13, line 46p afro-r "systems of"insert the M; Column lo, line 8, for "oompriss" rsa@ .signed and ySealedthis 25th day @August i959.

Attest:

ROBERT C. WATSON Attesting Officer. Corm'lssioner of Patents

